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The closed-form sum of \(12 \left[ 1^2 \cdot 2 + 2^2 \cdot 3 + \ldots + n^2 (n+1) \right]\)


for \(n \geq 1\) is \(n(n+1)(n+2)(an+b)\)  Find \(an + b\)

 May 7, 2021
 #1
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The sum is n(n + 1)(n + 2)(4n + 1), so an + b is 4n + 1.

 May 7, 2021

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